The invention is based on an anti-skid control system. An anti-skid control system of this kind is known (German Offenlegungsschrift No. 1 755 965). In this known anti-skid control system, a pressure fluid is pumped back into a brake line from a relief line, disposed between the valve assembly of at least one wheel brake cylinder and the feed device, by means of a return device actuatable by a hydraulically triggered switching valve. It can be assumed that the switching valve, triggered by a predetermined relief pressure, and that in the event of anti-skid control, which very rapidly supplies a large amount of pressure fluid to the relief line, the associated feed device will react too slowly and will not allow the fast reduction in pressure that is required.